No abstract

The cubic hexapod, or Stewart platform, has become a popular approach to the problem of active control of vibration because it can be placed directly in the path of vibration transmission and provides 6-axis isolation. Typically the control approach has been to use classical techniques with a variety of sensors, but a multiinput, multi-output (MIMO) approach holds much promise. Before designing controllers, however, it is important to know a great deal about the model, particularly the zero structure. Information on the size and position (minimum vs. non-minimum phase) of system zeros is necessary in predicting the opportunity for robustness recovery in MIMO controller design. A technique known as special coordinate basis (SCB) was applied to a model of a hexapod that was constructed by the Hood Technology Corporation and the University of Washington. Examining sensors including load cells, geophones and linear variable differential transformers (LVDT's), it was found that, though the use of other sensors offers some significant advantages for MIMO control over classical approaches, the well known robustness recovery tool known as loop transfer recovery (LTR), cannot be used because of the presence of small non-minimum phase zeros. IntroductionVibration isolation is a topic that has received a great deal of attention over the past 20 years or so. This problem has historically been handled using passive techniques. However, as systems, particularly those in space, continue to mature and require even greater precision and quieter environments, the implementation of active control approaches will be required to achieve desired performance levels. Currently, the primary drivers for this technology are the spacebased interferometry missions planned by the Jet Propulsion Laboratory (JPL) to fly after the tum of the century.One promising approach to this problem that is being investigated in a number of studies [I-6,9] is the six strut cubic hexapod. One of the most important advantages of this approach, using systems similar to the one shown in Figure 1, is that it allows a vibration isolator with six axis capability to be placed directly in the path of the disturbance. So rather than having to deal with vibration problems over the entire spacecraft, this system can isolate a "noisy" source, like a reaction wheel assembly (RWA), from an otherwise "quiet" spacecraft or conversely, it can create a "quiet" platform on a "noisy" spacecraft.With few exceptions, the control strategy used for this type of system has been classical [ 1-3,5,6,9]. In a cubic hexapod each strut is designed to be orthogonal to the one next to it, and because of this a single-input, single-output (SISO) loop can be closed around each strut using six identical controllers, each working independently. This can be done with any number of combinations of actuators and sensors. But all of these SISO approaches suffer from the same problem, and that is that, even though the struts are all orthogonal, thereby minimizing the effect of one strut on one nex...